Spectrum-Revealing Cholesky Factorization for Kernel Methods

TL;DR

This paper introduces a spectrum-revealing Cholesky factorization method for kernel matrix approximation, offering a reliable and faster alternative to existing methods for large-scale machine learning applications.

Contribution

The paper presents a novel spectrum-revealing Cholesky factorization and an efficient randomized algorithm, improving speed while maintaining effectiveness in kernel matrix approximation.

Findings

The new method is as effective as existing Cholesky-based kernel methods.

The randomized algorithm significantly reduces computation time.

Numerical experiments confirm the method's efficiency and reliability.

Abstract

Kernel methods represent some of the most popular machine learning tools for data analysis. Since exact kernel methods can be prohibitively expensive for large problems, reliable low-rank matrix approximations and high-performance implementations have become indispensable for practical applications of kernel methods. In this work, we introduce spectrum-revealing Cholesky factorization, a reliable low-rank matrix factorization, for kernel matrix approximation. We also develop an efficient and effective randomized algorithm for computing this factorization. Our numerical experiments demonstrate that this algorithm is as effective as other Cholesky factorization based kernel methods on machine learning problems, but significantly faster.